The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  X  1  X  1  1  1  1  1  X  1  X  1
 0 2X  0  0  0  0  0  0  0  0 2X 2X  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X
 0  0 2X  0  0  0  0  0  0 2X 2X 2X  0 2X 2X  0  0 2X  0 2X 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0  0  0 2X
 0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X 2X  0  0  0  0 2X  0 2X 2X 2X  0 2X 2X 2X  0  0  0  0
 0  0  0  0 2X  0  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X 2X
 0  0  0  0  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X 2X
 0  0  0  0  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X
 0  0  0  0  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0 2X  0 2X 2X 2X  0 2X  0  0  0

generates a code of length 35 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+24x^28+4x^29+53x^30+24x^31+34x^32+60x^33+30x^34+1616x^35+29x^36+60x^37+18x^38+24x^39+26x^40+4x^41+17x^42+10x^44+9x^46+3x^48+1x^52+1x^58

The gray image is a code over GF(2) with n=280, k=11 and d=112.
This code was found by Heurico 1.16 in 0.093 seconds.